The lactose operon has served as the paradigm to study gene regulation. To understand more completely how the operon is regulated we have undertaken the crystallographic structure determination of (1) the lac repressor, (2) the repressor bound to inducer and (3) the repressor in a ternary complex with synthetic operator fragments of DNA plus an anti-inducer. The three dimensional structure of this protein and the complexes will allow us to address such questions as: (1) How does the repressor recognize specific sites on the DNA? (2) How do the inducers and anti-inducers affect the conformation of the repressor? (3) What role does structure play in the allosteric mechanism and how is it used to regulate gene expression? In addition, the three dimensional structure of the lac repressor will provide a framework for correlating and interpreting an extensive body of genetic and chemical data.